Plan: M0030M, LP2, 2017

Transkript

1 Plan: M0030M, LP2, 2017 Examiner: Norbert Euler, Division of Mathematics, TVM, LTU. Course Literature: R A Adams and C Essex (hereafter referred to as A&E) Calculus, 9-th Edition. D C Lay, S R Lay and J J Mc Donald (hereafter referred to as LL&M) Linear Algebra and its applications, 5-th Edition, 2015/2016. M Euler and N Euler (hereafter referred to as E&E) Problems, Theory and Solutions, Part 1: Euclidean Space (2nd edition) [Free online access to this ebook is available from the direct link: Computer Lab in Maple: This course also includes exercises in Maple. The Maple exercises and instructions are provided towards the end of this document. An introduction to Maple is given in Appendix A in E&E on pages Lectures on Linear Algebra: Lecture 1. Vectors and coordinates in 3-space: (A&E) Lecture 2. Vectors and coordinates in 3-space: 10.2 (A&E) Lecture 3. The cross product: 10.3 (A&E) Lecture 4. The cross product/lines and planes in R 3 : 10.3/10.4 (A&E) Lecture 5. More on planes and lines in R 3 : 10.4 (A&E) Lecture 6. More on planes and lines in R 3 : 1.5 (E&E) Lecture 7. Reserve Lecture 8. Systems of linear equations: 1.1 and 1.2 (LL&M) Lecture 9. Vector equations and Matrix equations: 1.3 and 1.4 (LL&M)

2 2 M0030M Lecture 10. Solutions of systems of linear equation: 1.5 (LL&M) Lecture 11. Maple and more on Solutions of systems of linear equation: 1.5 (LL&M) Lecture 12. Linearly independet set and Linear transformations: 1.7 and 1.8 (LL&M) Lecture 13. Linear transformations and standard matrices: 1.8 and 1.9 (LL&M) Lecture 14. Matrix operations and Inverse of square matrices: 2.1 and 2.2 (LL&M) Lecture 15. Invertible transformations: 2.3 (LL&M) Lecture 16. More on Linear Transformations: 4.1, 4.2, 4.3 (E&E) Lecture 17. Determinants: 3.1 and 3.2 (LL&M) Lecture 18. More on determinants and Cramer s rule: 3.3 (LL&M) and 2.5 (E&E) Lecture 19. Reserve Lectures on Integral Calculus: Lecture 20. Sums and areas of limits of sums: (A&E) Lecture 21. Riemann sums and the definite integral: 5.3 (A&E) Lecture 22. Properties of the definite integral: 5.4 (A&E) Lecture 23. The fundamental theorem of calculus: 5.5 (A&E) Lecture 24. The method of substitution: 5.6 (A&E) Lecture 25. The area of a plane region: 5.7 (A&E) Lecture 26. Reserve Lecture 27. Integration by parts: 6.1 (A&E) Lecture 28. Integration of rational functions: 6.2 (A&E) Lecture 29. Inverse substitution: 6.3 (A&E) Lecture 30. Improper integrals: 6.5 (A&E)

3 M0030M 3 Lecture 31. Reserve Lecture 32. Solids of revolution: Volumes by slicing: 7.1 (A&E) Lecture 33. Solids of revolution: Volumes by slicing: 7.2 (A&E) Lecture 34. Arc length and surface area: 7.3 (A&E) Lecture 35. Parametric curves: 8.2 (A&E) Lecture 36. Smooth parametric cureves and their slopes Slopes: 8.3, (A&E) Lecture 37. Arc length and areas of parametric curves: 8.4 (A&E) Lecture 38. Reserves Recommended Exercises and Repetitions: Linear Algebra:. Exercises 10.1 (A&E): 1, 3, 6, 9, 13, 15, 23. Exercises 10.2 (A&E): 1a, 1f, 1h, 2, 3, 13. Repetition on the dot product (E&E 1.1): Work through the solved Problems in Section 1.1. Do Exercises 1.6: 1a, 1b, 1c, 1d, 1e, 1f. Exercises 10.3 (A&E): 1, 3, 4, 5, 7, 9, 13, 17. Repetition on the cross product (E&E 1.2): Work through the solved Problems in Section 1.2. Do Exercises 1.6: 2, 3. Exercises 10.4 (A&E): 3, 4, 5, 7, 9, 15, 17, 21, 27, 28, 29. Repetition on planes and lines (E&E 1.3, 1.4, 1.5): Work through the solved Problems in Sections 1.3, 1.4, 1.5. Do Exercises 1.6: 5, 7, 8, 9, 10.

4 4 M0030M Exercises 1.1 (LL&M): 1, 7, 9, 11, 13, 15, 17, 19. Exercises 1.2 (LL&M): 1, 3, 7, 11, 17, 19, 23,, 24 25, 29, 31. Exercises 1.3 (LL&M): 5, 9, 11, 13, 15, 17, 20, 21. Exercises 1.4 (LL&M): 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21. Exercises 1.5 (LL&M): 1, 3, 5, 7, 11, 13 Repetition on Gauss elimination (E&E 2.4, 2.6 and 2.7): Work through the solved Problems in Sections 2.4, 2.6 and 2.7. Do Exercises 2.8: 6, 7, 9, 11, 14a, 17. Exercises 1.7 (LL&M): 1, 5, 9, 13, 33, 35, 37. Repetition on Spanning Sets and Linearly Independent Sets (E&E 3.1, 3.2 and 3.3): Work through the solved Problems in Sections 3.1, 3.2 and 3.3. Do Exercises 3.4: 2, 3, 5, 6, 8. Exercises 1.8 (LL&M): 1, 3, 5, 9, 11, 17, 19, 32. Exercises 1.9 (LL&M): 1, 3, 5, 7, 19, 21. Exercises 2.1 (LL&M): 1, 3, 5, 7, 9. Exercises 2.2 (LL&M): 1, 5, 7, 19, 31, 32. Exercises 2.3 (LL&M): 1,3, 7, 33. Repetition on Linear Transformations and Standard Matrices (E&E 4.1, 4.2 and 4.3): Work through the solved Problems in Sections 4.1, 4.2 and 4.3. Do Exercises 4.4: 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 13. Exercises 3.1 (LL&M): 1, 11, 25, 27, 41. Exercises 3.2 (LL&M): 5, 9, 19, 25, 29, 31, 42

5 M0030M 5 Exercises 3.3 (LL&M): 3, 5, 7, 19, 27. Repetition on Matrix Operations, Determinants and Cramer s Rule (E&E 2.1, 2.2, 2.3, 2.5): Work through the solved Problems in Sections 2.1, 2.2, 2.3 and Do Exercises 2.8: 1, 3, 4, 5, 12. Integral Calculus Exercises 5.1 (A&E): 1, 9, 21. Exercises 5.2 (A&E): 1, 5, 9. Exercises 5.3 (A&E): 1, 9, 11, 13. Exercises 5.4 (A&E): 1, 3, 7, 13, 15, 27, 29, 33. Exercises 5.5 (A&E): 7, 11, 13, 15, 17, 21, 23, 25, 27, 28, 31, 33, 39, 41. Exercises 5.6 (A&E): 1, 3, 5, 7, 9, 13, 15, 21, 23, 27, 41, 43, 47. Exercises 5.7 (A&E): 3, 5, 7, 9, 11, 13, 15, 17, 18, 25, 29. Exercises 6.1 (A&E): 1, 3, 5, 7, 9, 13, 21, 23, 29, 31. Exercises 6.2 (A&E): 1, 3, 5, 7, 9, 11, 13, 15, 17, 23, 25, 30, 31. Exercises 6.3 (A&E): 1, 3, 5, 9, 11, 17, 29, 31, 41, 43, 45. Exercises 6.5 (A&E): 1, 5, 9, 15, 19, 23, 25, 31, 33, 41. Exercises 7.1 (A&E): 1, 3, 5, 7, 9, 11, 21. Exercises 7.2 (A&E): 1, 3, 5, 11. Exercises 7.3 (A&E): 1, 3, 5, 7, 9, 11, 22, 23, 26. Exercises 8.2 (A&E): 3, 5, 13. Exercises 8.3 (A&E): 1, 3, 5, 7, 9, 11, 13 Exercises 8.4 (A&E): 1, 3, 5, 7, 9, 10, 11, 13

6 6 M0030M Repetition on Methods of Integration See Appendix B, pages in N Euler A first course in ordinary differential equations, July 2015 [Free online access to this ebook is available at bookboon.com by the following direct link: bookboon.com/se/a-first-course-in-ordinary-differential-equations-ebook] Maple Exercises in Linear Algebra: Use Maple to solve the following four Problems and write your results and explanations clearly in a written presentation. Please follow the Rules and Instructions as listed below. You ll find the following Exercises in E&E: Problems, Theory and Solutions, Part 1: Euclidean Space. An introduction to Maple is given in Appendix A (pages ) Problem 1: 2.8. Exercise 8, page 107. Problem 2: 2.8 exercise 18, page 112. [Hint: Work through the solved Problem on page 94. Problem 3: 3.4. Exercise 9a, page 140. Problem 4: 4.4. Exercise 18, page 192. [Hint: Work through the solved Problem on page 192. Regler och instruktioner för Maple-momentet: 1. För att bli godkänd på Maple-momentet av kursen M0030M måste studenterna lösa uppgifterna i detta dokument med hjälp av Maple. 2. Studenterna får jobba enskilt eller i en grupp bestående av högst 3 personer. En lektion om Maple kommer att ges av studenternas lärare och inkluderar en kort introduktion av Maple och information om uppgifterna. Studenterna förväntas kunna lösa uppgifterna på egen hand. 3. Flera laborationer har blivit schemalagda för denna kurs i E-huset. Mer information angående schemat finns tillgängligt på LTU s hemsida. 4. Det finns bara två betyg på detta moment. Studenterna kan antingen bli godkända eller icke godkända. För att bli godkänd måste studenterna lösa alla problem korrekt och presentera resultatet väl i en skriftlig redogörelse. Det är viktigt att studenterna anger sin e-post adress i den skriftliga redogörelsen, skriver datum för inlämningen och sitt fullständiga namn, samt vilket program de studerar, t.ex. Rymdteknik.

7 M0030M 7 Studenternas lärare bestämmer hur rapporten skickas in, t.ex. bifogad i mail eller en utskriven på papper. Varje lärare kommer att ge instruktioner under lektionen hur studenterna ska lämna in den skriftliga redogörelsen. OBS! Skriftlig redogörelse kan ej bli inskickad via canvas. Rättningen och bedömningen av studenternas skriftlig redogörelse kommer att utföras av läraren som undervisar gruppen. Om läraren inte är nöjd med skriftlig redogörelse så kommer hen att ge dessa studenter instruktioner för förbättringar. 5. Under den sista lektionen kommer läraren med en lista med studenternas betyg för laborationen. OBS! Studenterna är ansvariga för att själva kontrollera att deras betyg skrivits in korrekt på listan under den sista lektionen. 6. Varje lärare har en skyldighet att rapportera in varje misstanke om fusk till disciplinnämden för vidare utredning och åtgärder. Följande är ett example på fusk. Varje form av kopiering av resultat och lösningssteg till någon av uppgifterna från laborationen. Detta gäller såväl kopiering av andra personers lösningar och lösningar som möjligen kan hittas på internet. 7. Alla studenter ska lämna in sina skriftliga redogörelser senast den 15 december Inga skriftliga redogörelser kommer att intas efter 15 december Den student som inte lämnar in sin rapport senast detta datum kommer automatiskt att bli underkänd denna omgång. Nästa omgång kommer att vara maj Studenterna kommer då att få nya uppgifter för labben. Rules and Instructions for the Maple assignments: 1. Students must solve the Maple problems listed in this document by using the program Maple. 2. Students can work in groups consisting of maximum three student members and hand in a joint written presentation. One lecture on Maple has been scheduled for each group during the course and this lecture will include a short introduction to Maple and some information regarding the exercises. The students are expected to make use of the information given in the Appendix in E&E and the online help included in the Maple package which is installed on the LTU computers. 3. Several lab sessions have been scheduled for this course in the E-building and students can attend any of those sessions, provided space is available in the computer room. Please visit the LTU schema website for details on the lab schedule. 4. Two grades are possible for the Maple computer lab, namely a Pass or a Fail. In order to pass the Maple computer lab the student must solve the listed problems correctly and present the results neatly in a written presentation. The written presentation should contain all Maple steps used in solving the problems and the solutions should moreover be described in the written presentation. Students can use Word or Latex to write their written presentation. Students must write their full name and surname, a contact address, the date of

8 8 M0030M submission, as well as the programme in which they are studying, e.g. Rymdteknik, on the front page of their written presentation. The form of submission, i.e. in printer form or as an attachement by , will be determined by the particular teacher. Most teachers prefer a paper printed version of the written presentation, but exact information regarding the submission will be given by the teacher during the lecture. Please note that the written presentations should not be submitted via the canvas system. The evaluation and grading of the written presentations will be done by the teacher who is responsible for the particular group that he/she is teaching. If the teacher is not satisfied with the solutions handed in by the student(s), then the teacher will provide the student(s) with instructions for improvements. 5. During the last lecture, the teachers will bring with them a list that will contain the grades of the written presentations for the students in their group. It is the students own responsibility to verify with their teacher that their grades have been recorded correctly on that list during the last lecture in May. 6. Teachers are obliged to report any suspected foul play of the laboration to the university disciplinary office for further investigation and conviction. The following is an examples of foul play of the laboration: the copying, in any form or by any means, of results or program steps of the solutions of any hereby listed exercise, from other persons or student participants or from an internet site. 7. All students must submit their written presentations to their teacher at the latest on the 15th of December No lab results will be accepted after this date. Those students that have not handed in their written presentations by this date will automatically fail this Maple computer lab. The next opportunity to do the Maple computer lab will then be in May 2018 and different exercises will be provided.